Computing linkage



r x, r

A. SVOBODA Jan. 18, 1949.

COMPUTING LINKAGE 2 Sheets-Sheet 1 Filed Jan. 15, 1946 INYENTOR. ANTONIN SVOBODA ATTbRNEY where X isthe displacement of one of the mem- Patented Jan. 18, 1949 UNITED STATES PATENT OFFICE COMPUTING LINKAGE Antonin Svoboda, Cambridge, Mass, assignor, by mesne assignments, to the United States of America as represented by the Secretary of the ame-L V Application January 15, 1946, Serial No. 641,345

2 Claims. (01. 235-615) a 1 2 This invention relates to a mechanical comthat displacement of the output angle thereof is puter for performing dividing computations and proportional to Y where more particularly to a mechanical divider in 1 gvlhgactillie quotient determined is positive in 5 (l+ 0402X)2 where X is the displacement of the input section of the device from its zero position. The curve of Fig. 2 is a plot of this function over the por- For general information purposes in connection with the present invention, reference is made to the textbook, Computing Mechanisms and Linkages, vol. 27, by Antonin svoboda tion thereof defined by a range of values of X Massachusetts Institute of Technology Radia between zero and 29.9. The ordinates of the on Laboratory Series, First Edition 1948, curve are expressed both in terms of seconds and Graw Hm Book Company, hm percent of range of operation, and the abscissa An object of this invention is to provide a are exprejgsed terms of f 001 mechanical computer and more particularly to mcasmed both percent of range of opef'atlon provide Such a computer for performing dividing 1 and in units. The curve of the function is computations regular in form over the operating range and A particular object of this invention is to prothus lends Itself to mechamzatlonvide a mechanical computer for solving the Referfing to 1 ereis shown a support equation I0 having curved and straight swinging mem- 2Q bers and 2i pivoted to support 7 at points A y= and B, respectively,

A link 22 operatively connects point E of mem- Further objects and advantages of this inven- 55 :2 2 gi gg gg g l gg g $3 gg tion, as well as 1ts construction, arrangeme eluniformly calibrated in positive values of X from and operation, Will be apparent from the follow- X=O is affixed adjacent the sndeway 24 to mg description. and i in fonnection with indicate input values of X into the mechanism. the .acwmpimymg drawmg'm The free ends of members 20 and 2] are joined Figure 1 15 assembly drawing of q g in a pivotal manner by means of a link 25 at points constructed in accordance with the principles C and D respectively It is to be understood of tthls .Wentwn; that all of the connections referred to are pivot 2 1s a curve of the equatlon connections so as to allow relative movement between the various connected members, unless it is expressly indicated that the connections are rigid in character.

3" The relative dimensions of the various links and members forming the computer are such that if displacement of pin 23 is proportional to X,

then the angular displacement of member 2| el mz r n 51 .1 sbem nq h pl a t0 the pmss g over the range of operation of the linkage of the present invention; and

Fig. 3 is a curve of the theoretical precision of the computer of the present invention over its M As stated, the purpose of this invention is to 0 1 provide a mechanical computer for solving the (1+.0402A') equation a a which may be represented by the term Y. Posi- Y= 1 tioned beneath member 2| and in cooperation (l+0.402X) therewith is a uniformly calibrated arcuate scale 32 for indicating values of Y. As shown bers of t e Co p e from i s e o position. A X=0 position on scale 30, the pointer at the m c a l e odymg y invention consists of extremity of member 2| is adjacent the Y=1 & linkage y e -having Such relative dimensions calibration on scale 32 in accordance with the in Fig. 1, for a setting of pin 23 adjacent the? In order that the above relationship may be true, the relative dimensions of the device stated in terms of unity (1) as a basis of measurement are as follows:

Horizontal distance from pivot point A to pivot point B 1.0000 Vertical distance from pivot point A to pivot point B Length of member 20 from pivot point A to pivot point C *,I1$1080 Length of member 20 from pivot point A to pivot point E .2500 Angle included between lines AC and AE of member 20 107 Length of member 2| .5010 Length of member 22 1.0000

Length of member 25 19404 point A to point C, link 2i and link 25.

The device may be considered to consist'of an input section and an output section, the input being represented by links 22 and that portion of member 20 extending from pivot point A to point E, and the output section being represented by that portion of member 20 extending from In the operation of the device, if the displacement of pin 23 from the zero point is proportional to X, then the angular displacement of link 2| about pivot point B will be proportional to which may be defined as Y. The position of pin 23 in the figure corresponds to the X= position. The displacement of this pin to the right for a given value of X is .11245 times the value of X multiplied by the dimensional unit for the input section. It has heretofore been stated that the output angle is proportional to Y. The actual expression for the output angle is .13731 times the quantity (825Y). It is noted that the operating range of member 20, that is the input range, and the operating range of member 2!, that is the output range,-for best precision with this mechanism is 90.

Although member 20 has been illustrated as a single curved member, it will readily be understood that this member may easily be replaced by a pair of links of dimensions AC and A-E, fixedly joined together at an angle of 107,

The curve of Fig. 3 indicates the theoretical precision of the present linkage over the range of operation thereof as determined bythe curve of Fig. 2. The abscissa-s of the curve show the class B error'of the mechanism in terms of units of Y and in percentage. Class B error is that defined as inherent in the linkage by reasonof lengths of elements used, orientation, etc., and does not include error due to backlash between elements and such mechanical errors. It will be noted that except for small portions of the operating range when the values of X are small,

the error of the linkage does not exceed more than approximately .75% of the value of flX) over about 97% of the operating range.

While this computer has been disclosed and described as a computer independent of any associated mechanism, the computer has found particularly useful application in connection with gun training systems and ballistics computing apparatus in which it has been found to be necessary to develop a movement proportional to the expression where X is the displacement of one member of such apparatus.

While a particular embodiment of my invention has been disclosed and described, it is to be understood that various changes and modifications may be made therein without departing from the spirit and scope of the following claims.

What is claimed is:

1. A mechanical computer for computing th expression comprising a support, a first swinging member pivoted to said support, a second swinging member pivoted to said support, a slide member slidably mounted on said support, a first link operatively connecting one end of said second swinging member and said slide member, and a second link operatively connecting said first and second swinging members, said links and swinging members having the following relative dimensions where the basis of measurement is taken as unity (1) Length of first swinging member .5010 Length of second swinging member from the pivot point thereof to one end .2500

Length of second swing member from the pivot point to the opposite end 1.1080 Angle included lines connecting the pivot point of said second swinging member and the opposite ends thereof 107 Length of said first link 1000 Length of said second link 1.9404

the pivot points of said swinging members being so disposed with respect to each other that angu lar displacement of said first swinging member is proportional to where X represents the displacement of said slide member from the zero position thereof.

2. A linkage mechanism for computing the empirical function where X is an independent input variable in seconds and Y is the output of said mechanisms measured in units, said mechanism comprising,

a supporthavingalongitudinal-axis-and a slidefirst unpivoted end of said bell-crank, and a second link operatively connecting the second unpivoted end of said bell-crank and the unpivoted end of said swinging member, said links and swinging members having the following relative dismensions and orientations where the basis of comparison is taken as unity:

Length of said swinging member .5010 Length of said bell-crank from the knee thereof to the said first unpivoted end thereof .2500 Length of said bell-crank from the knee thereof to the said second unpivoted end .thereof 1.1080 Angle included between lines drawn from the knee of said bell-crank to the said first and second unpivoted ends thereof 107 Length of said first link 1.000 Length of said second link 1.9404 Distance along said axis between the pivot points of said bell-crank and said swinging member 1.000 Distance along said axis between the pivot point of said bell-crank and the position of said slidable pin, where the value of X 0 .7849 Angie measured clockwise between a line joining the pivot point and the said the aforementioned dimensions and orientation providing that the angular displacement of said swinging member is proportional to the displacement of said slidable pin from the X 0 position thereof in accordance with the expression ANTONIN SVOBODA.

REFERENCES CITED The following references are of record in the 20 file of this patent:

UNITED STATES PATENTS Number Name Date 2,394,180 Imm Feb. 5, 1946 FOREIGN PATENTS Number Country Date 113,136 Great Britain Feb. 7, 1918 

